Basic 7 Maths Mid-Term Assignment

TRINITY INTERNATIONAL COLLEGE

TRINITY HILLS, OFADA

THIRD TERM 2017/2018 SESSION

MATHEMATICS MID TERM ASSIGNMENT FOR BASIC 7

INSTRUCTIONS:   Answer ALL the questions. 
                                  Clearly show all workings leading to the answers. 
                                  Answer the questions in your assignment note.

1          The shoe sizes of 20 men are given below.

            9          6          10        8          11        9          10        7          8          8

            7          6          7          8          8          6          7          10        11        8

(a)        Prepare a tally-frequency table for the data

(b)        Calculate the mean of the data.

(c)        Find the median

(d)        What is the mode?

(e)        What is the range of the shoe sizes?

(f)         What percentage of the men wear size 8?

(f)        What is the probability that a man picked at random wears size 8?

2.          Measure the length and breadth of your bed in cm. If your mother placed a box measured 40cm by 70cm on the bed as shown below. Find the area not covered by the box.

                                           

 

STATISTICS

STATISTICS

Statistics is a method of collecting, organizing and analyzing data.

Data means raw fact or basic information usually in number form. Singular for Data is Datum.

Statistics is useful in our everyday life for decision making, prediction and information.

Data Organisation and Frequency Tables

Data can be arranged in an increasing or decreasing order of magnitude to make them more meaningful. The frequency of an event (anything) is the number of times it occurs in a given set of data.

Tally system makes use of strokes to represent frequencies.

Example

            An English teacher gave a spelling test to her class of 30 pupils and obtained the following data of their scores

                        2          3          5          3          4          6          8          8          2          6

                        4          7          4          5          9          9          7          4          4          7

                        3          3          6          8          6          7          6          3          5          3

            Represent the data on a tally-frequency table.

Steps

(i)         Make 3 columns for marks, tally and frequency respectively.

(ii)        List out the different possible marks in the marks column.

(iii)       Pick the items in the data one after the other and make tally marks in each case at the appropriate row to represent the data.

(iv)       Count the number of tally against each mark, this gives the frequency of each mark.

Marks	Tally	Frequency
2	||	2
3	|||| |	6
4	||||	5
5	|||	3
6
7
8
9

Statistics

What Are Statistics?

Learning about the different kinds of statistics

Learning about variables

Understanding the steps in statistical reasoning

Learning several uses for statistical reasoning

For many people, statistics means numbers—numerical facts, figures, or information. Statistics is about data. Data consists of information about statistical variables. 

There are two types of variables: 

Quantitative variables are variables that can be measured or described by values, such as height. 

Categorical variables have values that are categories, such as type of pet. The data for these variables are usually counts or frequencies of the numbers for each category.

Reports of industry production, baseball batting averages, government deficits, and so forth, are often called statistics. To be precise, these numbers are descriptive statistics because they are numerical data that describe phenomena. 

Descriptive statistics are as simple as the number of children in each family along a city block or as complex as the annual report released from the U.S. Department of the Treasury.

Data

What is Data?

Data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Qualitative vs Quantitative

Data can be qualitative or quantitative.

• Qualitative data is descriptive information (it describes something)
• Quantitative data is numerical information (numbers)

Quantitative data can be :

• Discrete data can only take certain values (like whole numbers)
• Continuous data can take any value (within a range)

Put simply: Discrete data is counted, Continuous data is measured

Example: What do we know about Arrow the Dog?

Qualitative:

• He is brown and black
• He has long hair
• He has lots of energy

Quantitative:

• Discrete:
  • He has 4 legs
  • He has 2 brothers
• Continuous:
  • He weighs 25.5 kg
  • He is 565 mm tall

To help you remember think "Quantitative is Quantity"

More Examples

Qualitative:

• Your friends' favorite holiday destination
• The most common given names in your town
• How people describe the smell of a new perfume

Quantitative:

• Height (Continuous)
• Weight (Continuous)
• Petals on a flower (Discrete)
• Customers in a shop (Discrete)

Collecting

Data can be collected in many ways. The simplest way is direct observation.

Example: Counting Cars

You want to find how many cars pass by a certain point on a road in a 10-minute interval.

So: stand near that road, and count the cars that pass by in 10 minutes.

You might want to count many 10-minute intervals at different times during the day, and on different days too!

We collect data by doing a survey.

Census or Sample

A Census is when we collect data for every member of the group (the whole "population").

A Sample is when we collect data just for selected members of the group.

Example: 120 people in your local football club

You can ask everyone (all 120) what their age is. That is a census.

Or you could just choose the people that are there this afternoon. That is a sample.

A census is accurate, but hard to do. A sample is not as accurate, but may be good enough, and is a lot easier.

Language

Data or Datum?

The singular form is "datum", so we say "that datum is very high".

"Data" is the plural so we say "the data are available", but data is also a collection of facts, so "the data is available" is fine too.

Divisibility by Seven

Everyone learns in grade school some simple tests for divisibility by small numbers such as 2, 3, 5, and 9. But far less well-known are some simple divisibility tests for the number 7. Here are a couple: Test #1. Take the digits of the number in reverse order, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary. Add the products. This sum has the same remainder mod 7 as the original number! Example: Is 1603 divisible by seven? Well, 3(1)+0(3)+6(2)+1(6)=21 is divisible by 7, so 1603 is. Test #2. Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7. Example: 1603 -> 160-2(3)=154 -> 15-2(4)=7, so 1603 is divisible by 7. See the reference for more tests and more references. Presentation Suggestions: Do examples as you go! Perhaps remind students of the divisibility test for 9 before presenting these. If you are teaching a course, you may wish to assign their proofs as an exercise! The Math Behind the Fact: Here's a hint on how to prove them. For the first test, note that (mod 7), 1==1, 10==3, 100==2, 1000==6, etc. For the second test, note that (mod7), 10A+B==10*(A-2B). The second trick mentioned here can be modified to check for divisibility by other primes. For example, to check divisibility by 13, take the last digit, multiply by 4 and add to the truncated portion. To check divisibility by 19, double the last digit and add. In fact, for any prime p, there exists some integer k such that divisibility by p can be ascertained by multiplying the unit's digit by k and adding (or subtracting) from the truncated portion of the numeral.

Divisibility Rules

Divisibility Rules

The following set of rules can help you save time in trying to check the divisibility of numbers.

A number is divisible by	if
2	it ends in 0, 2, 4, 6, or 8
3	the sum of its digits is divisible by 3
4	the number formed by the last two digits is divisible by 4
5	it ends in 0 or 5
6	it is divisible by 2 and 3 (use the rules for both)
7	(no simple rule)
8	the number formed by the last three digits is divisible by 8
9	the sum of its digits is divisible by 9

Example 1

1. Is 126 divisible by 3? Sum of digits = 9. Because 9 is divisible by 3, then 126 is divisible by 3.
2. Is 1,648 divisible by 4? Because 48 is divisible by 4, then 1,648 is divisible by 4.
3. Is 186 divisible by 6? Because 186 ends in 6, it is divisible by 2. Sum of digits = 15. Because 15 is divisible by 3, 186 is divisible by 3. 186 is divisible by 2 and 3; therefore, it is divisible by 6.
4. Is 2,488 divisible by 8? Because 488 is divisible by 8, then 2,488 is divisible by 8.
5. Is 2,853 divisible by 9? Sum of digits = 18. Because 18 is divisible by 9, then 2,853 is divisible by 9.

Integers

Integers

The term integers refers to all the whole numbers together with their opposites—not fractions or decimals.

For example, … –3, –2, –1, 0, 1, 2, 3, … are integers.

On a number line, numbers to the right of 0 are positive. Numbers to the left of 0 are negative, as shown in Figure 1.

 Number line showing integers.

This figure shows only the integers on the number line.

Given any two numbers on a number line, the one on the right is always larger, regardless of its sign (positive or negative).

When adding two integers with the same sign (either both positive or both negative), add the integers and keep the same sign.

Add the following.

When adding two integers with different signs (one positive and one negative), subtract the integers and keep the sign on the one with the larger value.

Add the following.

Integers may also be added “horizontally.”

Add the following.

+8 + 11

–15 + 7

5 + (–3)

–21 + 6

+8 +11 = +19

–15 + 7 = –8

5 + (–3) = +2

–21 + 6 = –15

To subtract positive and/or negative integers, just change the sign of the number being subtracted and then use the rules for adding integers.

Subtract the following.

Subtracting positive and/or negative integers may also be done “horizontally.”

Subtract the following.

+12 – (+4)

+16 – (–6)

–20 – (+3)

–5 – (–2)

+12 – (+4) = +12 + (–4) = 8

+16 – (–6) = +16 + (+6) = 22

–20 – (+3) = –20 + (–3) = –23

–5 – (–2) = –5 + (+2) = –3

If a minus precedes a parenthesis, it means that everything within the parentheses is to be subtracted. Therefore, using the same rule as in subtraction of integers, simply change every sign within the parentheses to its opposite and then add.

Subtract the following.

9 – (+3 – 5 + 7 – 6)

20 – (+35 – 50 + 100)

9 – (+3 – 5 + 7 – 6) = 9 + (–3 + 5 – 7 + 6)

= 9 + (+1)

= 10

20 – (+35 – 50 + 100) = 20 + (–35 + 50 – 100)

= 20 + (–85)

= –65

Or, if you can, total the numbers within the parentheses by first adding the positive numbers together, next adding the negative numbers together, then combining, and finally subtracting.

Subtract the following.

9 – (+3 – 5 + 7 – 6)

20 – (+35 – 50 + 100)

3 – (1 – 4)

Remember: If there is no sign given, the number is understood to be positive.

or 

To multiply or divide integers, treat them just like regular numbers but remember this rule: An odd number of negative signs produces a negative answer. An even number of negative signs produces a positive answer.

Multiply or divide the following.

The numerical value when direction or sign is not considered is called the absolute value. The absolute value of a number is written | |. Therefore, |3| = 3 and |–4 | = 4. The absolute value of a number is always positive except when the number is 0. The absolute value of zero is zero, | 0 | = 0.

Give the value.

|5|

| –8|

|3 – 9|

3 – | –6|

|5| = 5

|–8| = 8

|3 – 9| = |–6| = 6

3 – |–6| = 3 – 6 = –3

Note: Absolute value is taken first or work is done within absolute value brackets